The sequence of random numbers generated by a single Random instance is supposed to be uniformly distributed. By creating a new Random instance for every random number in quick successions, you are likely to seed them with identical values and have them generate identical random numbers. Of course, in this case, the generated sequence will be far from uniform distribution.

For the sake of completeness, if you really need to reseed a Random, you'll create a new instance of Random with the new seed: